It is nothing weird about this really. Higher taxed countries are able to offer better public education and health care which gives the lesser of actually stand a chance of making it.
In the US the system is especially rigged. There is no free school choice, so you are forced to go to the public school in your shitty neighborhood if you are poor, while the rich through never ending donations enjoy schools with abundant resources. And even if the schools were good you would be screwed before you even get in, because the US does not offer quality child care to poor people. Research shows the years before school is the most important for future development.
I live in a poorer area of Oslo, but I could if I wanted to send my kids to the schools in the richest part of town without any extra cost to me. But it isn't really important as school quality is pretty even, through proper public funding rather than relying on private donations. Also we get subsidized child care of a quality that typically only upper middle class buy in the US.
If you don't even the playing field in a persons early years you are not going to see much social mobility.
http://www.usgovernmentspending.com/us_20th_century_chart.ht...
Note the ever larger share of government spending as a percentage of the GDP. This doesn't happen unless taxes, in one way or another, go up.